Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection

We study hexagon patterns in non-Boussinesq convection of a thin rotating layer of water. For realistic parameters and boundary conditions we identify various linear instabilities of the pattern. We focus on the dynamics arising from an oscillatory side-band instability that leads to a spatially disordered chaotic state characterized by oscillating (whirling) hexagons. Using triangulation we obtain the distribution functions for the number of pentagonal and heptagonal convection cells. In contrast to the results found for defect chaos in the complex Ginzburg-Landau equation and in inclined-layer convection, the distribution functions can show deviations from a squared Poisson distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J. Physic

Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation

It has been shown in our previous publication (Blawzdziewicz,Cristini,Loewenberg,2003) that high-viscosity drops in two dimensional linear creeping flows with a nonzero vorticity component may have two stable stationary states. One state corresponds to a nearly spherical, compact drop stabilized primarily by rotation, and the other to an elongated drop stabilized primarily by capillary forces. Here we explore consequences of the drop bistability for the dynamics of highly viscous drops. Using both boundary-integral simulations and small-deformation theory we show that a quasi-static change of the flow vorticity gives rise to a hysteretic response of the drop shape, with rapid changes between the compact and elongated solutions at critical values of the vorticity. In flows with sinusoidal temporal variation of the vorticity we find chaotic drop dynamics in response to the periodic forcing. A cascade of period-doubling bifurcations is found to be directly responsible for the transition to chaos. In random flows we obtain a bimodal drop-length distribution. Some analogies with the dynamics of macromolecules and vesicles are pointed out.Comment: 22 pages, 13 figures. submitted to Journal of Fluid Mechanic

Convergence of invariant densities in the small-noise limit

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in the small-noise limit is frequently governed by power laws. In addition, a simple heuristic is proposed and found to correctly predict the power law exponent in exponentially mixing systems. In systems which are not exponentially mixing, the heuristic provides only an upper bound on the power law exponent. As this numerical study requires the computation of invariant densities across more than 2 decades of noise amplitudes, it also provides an opportunity to discuss and compare standard numerical methods for computing invariant probability densities.Comment: 27 pages, 19 figures, revised with minor correction

Thermoelectric enhancement in PbTe with K, Na co-doping from tuning the interaction of the light and heavy hole valence bands

The effect of K and K-Na substitution for Pb atoms in the rock salt lattice of PbTe was investigated to test a hypothesis for development of resonant states in the valence band that may enhance the thermoelectric power. We combined high temperature Hall-effect, electrical conductivity and thermal conductivity measurements to show that K-Na co-doping do not form resonance states but2 can control the energy difference of the maxima of the two primary valence sub-bands in PbTe. This leads to an enhanced interband interaction with rising temperature and a significant rise in the thermoelectric figure of merit of p-type PbTe. The experimental data can be explained by a combination of a single and two-band model for the valence band of PbTe depending on hole density that varies in the range of 1-15 x 10^19 cm^-3.Comment: 8 figure

Probing neutrino oscillations jointly in long and very long baseline experiments

We examine the prospects of making a joint analysis of neutrino oscillation at two baselines with neutrino superbeams. Assuming narrow band superbeams and a 100 kt water Cerenkov calorimeter, we calculate the event rates and sensitivities to the matter effect, the signs of the neutrino mass differences, the CP phase and the mixing angle \theta_{13}. Taking into account all possible experimental errors under general consideration, we explored the optimum cases of narrow band beam to measure the matter effect and the CP violation effect at all baselines up to 3000 km. We then focus on two specific baselines, a long baseline of 300 km and a very long baseline of 2100 km, and analyze their joint capabilities. We found that the joint analysis can offer extra leverage to resolve some of the ambiguities that are associated with the measurement at a single baseline.Comment: 23 pages, 11 figure

The SPICE carbon isotope excursion in Siberia: a combined study of the upper Middle Cambrian-lowermost Ordovician Kulyumbe River section, northwestern Siberian Platform

An integrated, high-resolution chemostratigraphic (C, O and Sr isotopes) and magnetostratigraphic study through the upper Middle Cambrian–lowermost Ordovician shallowmarine carbonates of the northwestern margin of the Siberian Platform is reported. The interval was analysed at the Kulyumbe section, which is exposed along the Kulyumbe River, an eastern tributary of the Enisej River. It comprises the upper Ust’-Brus, Labaz, Orakta, Kulyumbe, Ujgur and lower Iltyk formations and includes the Steptoean positive carbon isotopic excursion (SPICE) studied here in detail from upper Cambrian carbonates of the Siberian Platform for the first time. The peak of the excursion, showing δ13C positive values as high as+4.6‰and least-altered 87Sr/86Sr ratios of 0.70909, is reported herein from the Yurakhian Horizon of the Kulyumbe Formation. The stratigraphic position of the SPICE excursion does not support traditional correlation of the boundary between theOrakta and Labaz formations at the Kulyumbe River with its supposedly equivalent level in Australia, Laurentia, South China and Kazakhstan, where the Glyptagnostus stolidotus and G. reticulatus biozones are known to immediately precede the SPICE excursion and span the Middle–Upper Cambrian boundary. The Cambrian–Ordovician boundary is probably situated in the middle Nyajan Horizon of the Iltyk Formation, in which carbon isotope values show a local maximum below a decrease in the upper part of the Nyajan Horizon, attributed herein to the Tremadocian Stage. A refined magnetic polarity sequence confirms that the geomagnetic reversal frequency was very high during Middle Cambrian times at 7–10 reversals per Ma, assuming a total duration of about 10 Ma and up to 100 magnetic intervals in the Middle Cambrian. By contrast, the sequence attributed herein to the Upper Cambrian on chemostratigraphic grounds contains only 10–11 magnetic intervals

Non Mean-Field Quantum Critical Points from Holography

We construct a class of quantum critical points with non-mean-field critical exponents via holography. Our approach is phenomenological. Beginning with the D3/D5 system at nonzero density and magnetic field which has a chiral phase transition, we simulate the addition of a third control parameter. We then identify a line of quantum critical points in the phase diagram of this theory, provided that the simulated control parameter has dimension less than two. This line smoothly interpolates between a second-order transition with mean-field exponents at zero magnetic field to a holographic Berezinskii-Kosterlitz-Thouless transition at larger magnetic fields. The critical exponents of these transitions only depend upon the parameters of an emergent infrared theory. Moreover, the non-mean-field scaling is destroyed at any nonzero temperature. We discuss how generic these transitions are.Comment: 15 pages, 7 figures, v2: Added reference

Signatures of Electronic Nematic Phase at Isotropic-Nematic Phase Transition

The electronic nematic phase occurs when the point-group symmetry of the lattice structure is broken, due to electron-electron interactions. We study a model for the nematic phase on a square lattice with emphasis on the phase transition between isotropic and nematic phases within mean field theory. We find the transition to be first order, with dramatic changes in the Fermi surface topology accompanying the transition. Furthermore, we study the conductivity tensor and Hall constant as probes of the nematic phase and its transition. The relevance of our findings to Hall resistivity experiments in the high-$T_c$ cuprates is discussed.Comment: 5 pages, 3 figure